Modeling Part 1

I am back at modeling now. I am reading agent based modeling and individual based modeling by steven railback et.al. Thinking out loud,
it gets me thinking about the different types of models.

1. deterministic
2. non deterministic

and the subgategories goes like

1. deterministic
1.1 traditional mathematical models ( aggregate models)

2. non deterministic
2.1 statistical models ( sample models )
2.2 individual based models( individual models )

The models differ in the way they treat their variables. With traditional mathematical models, the variables are aggregates of similar type, eg number of people, height, age, etc. These are what we call quantities, infact quantity is an aggregate of similar things. Traditional mathematics models things by first quantifying and then finding equations that represent the quantity as it changes in time. Normally this is represented using differential equations( it can be done using plain functions however, with a note that some functions cannot be represented analytically hence has to be represented algorithmically, i.e numeric methods formulas.).

This contrast with individual based models which is individual focused. We are not interested in aggregates here, rather we are interested in individual states. State variables are properties of indivivuals not aggragates. Note an aggregate quantity like height or age may be a property of an individual but this is no representive of many individuals. With IBM, the model is run and emergent behaviour observed. This is behaviour should be similar to the target system. Now, its power come from being able to twirk the variables to study a certain effect. IBM has been likened to scientific method called experimentation.

It is my believe IBM has to be used together with traditional mathematical models, since experimental methods where used with mathematical models in the past.


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